The sum of a number and its reciprocal is 4.25; the number is :

1. 2 or $\dfrac{1}{2}$

2. 4 or $\dfrac{1}{4}$

3. $\dfrac{1}{5}$ or 5

4. $\dfrac{1}{3}$ or 3

Let the number be x.

Given,

Sum of a number and its reciprocal is 4.25

$\Rightarrow x + \dfrac{1}{x} = 4.25 \\[1em] \Rightarrow \dfrac{x^2 + 1}{x} = \dfrac{425}{100} \\[1em] \Rightarrow \dfrac{x^2 + 1}{x} = \dfrac{17}{4} \\[1em] \Rightarrow 4(x^2 + 1) = 17x \\[1em] \Rightarrow 4x^2 + 4 = 17x \\[1em] \Rightarrow 4x^2 - 17x + 4 = 0 \\[1em] \Rightarrow 4x^2 - 16x - x + 4 = 0 \\[1em] \Rightarrow 4x(x - 4) - 1(x - 4) = 0 \\[1em] \Rightarrow (4x - 1)(x - 4) = 0 \\[1em] \Rightarrow 4x - 1 = 0 \text{ or } x - 4 = 0 \\[1em] \Rightarrow 4x = 1 \text{ or } x = 4 \\[1em] \Rightarrow x = \dfrac{1}{4} \text{ or } x = 4.$

Hence, Option 2 is the correct option.